{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run 7.2.3-perceptron.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import FormatStrFormatter, LinearLocator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:13: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  del sys.path[0]\n"
     ]
    }
   ],
   "source": [
    "mpl.rcParams['legend.fontsize'] = 10\n",
    "# 1D S curves - positive weight\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca()\n",
    "x = torch.linspace(start=-10, end=10, steps=100)\n",
    "w = torch.tensor([1.0], dtype=torch.float32)\n",
    "b = torch.tensor([0.0])\n",
    "y = Perceptron(X=x.unsqueeze(dim=1), W=w.unsqueeze(dim=1), b=b, activation=torch.heaviside)\n",
    "ax.plot(x.squeeze(), y.squeeze(), label=\"w = 1 b = 0\")\n",
    "plt.title(\"positive weight yields S curve\", fontsize=16)\n",
    "ax.legend()\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:12: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  if sys.path[0] == '':\n"
     ]
    }
   ],
   "source": [
    "# 1D S curves - negative weight\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca()\n",
    "x = torch.linspace(start=-10, end=10, steps=100)\n",
    "w = torch.tensor([-1.0], dtype=torch.float32)\n",
    "b = torch.tensor([0.0])\n",
    "y = Perceptron(X=x.unsqueeze(dim=1), W=w.unsqueeze(dim=1), b=b, activation=torch.heaviside)\n",
    "ax.plot(x.squeeze(), y.squeeze(), label=\"w = -1 b = 0\")\n",
    "plt.title(\"negative weight yields laterally flipped S curve\", fontsize=16)\n",
    "ax.legend()\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:12: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  if sys.path[0] == '':\n"
     ]
    }
   ],
   "source": [
    "# 1D S curves - negative weight + shift\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca()\n",
    "x = torch.linspace(start=-10, end=10, steps=100)\n",
    "w = torch.tensor([-1.0], dtype=torch.float32)\n",
    "b = torch.tensor([5.0])\n",
    "y = Perceptron(X=x.unsqueeze(dim=1), W=w.unsqueeze(dim=1), b=b, activation=torch.heaviside)\n",
    "ax.plot(x.squeeze(), y.squeeze(), label=\"w = {} b = {}\".format(w, b))\n",
    "plt.title(\"change bias to shift curve\", fontsize=16)\n",
    "ax.legend()\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:16: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n",
      "  app.launch_new_instance()\n"
     ]
    }
   ],
   "source": [
    "# 1D towers (cybenko) - various W0\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca()\n",
    "x = torch.linspace(start=-10, end=10, steps=100)\n",
    "W0 = torch.tensor([[1.0], \n",
    "                   [-1.0]], dtype=torch.float32)\n",
    "b0 = torch.tensor([5.0, 5.0])\n",
    "W1 = torch.tensor([[1.0, 1.0]], dtype=torch.float32)\n",
    "b1 = torch.tensor([-1.5])\n",
    "y = MLP(X=x.unsqueeze(dim=1), W0=W0, W1=W1, b0=b0, b1=b1, activation0=torch.heaviside,activation1=torch.heaviside)\n",
    "ax.plot(x.squeeze(), y.squeeze(),\n",
    "        label=\"w0 = [1, -1] \\nb0 = [5, 5] \\nw1 = [1, 1] \\nb1 = -1.5\")\n",
    "plt.title(\"MLP generated rectangle\", fontsize=8)\n",
    "ax.legend()\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/torch/functional.py:568: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at  /Users/distiller/project/pytorch/aten/src/ATen/native/TensorShape.cpp:2228.)\n",
      "  return _VF.meshgrid(tensors, **kwargs)  # type: ignore[attr-defined]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:25: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "# 2D Step function in X-direction\n",
    "X = torch.linspace(start=-1, end=1, steps=100)\n",
    "Y = torch.linspace(start=-1, end=1, steps=100)\n",
    "gridX, gridY = torch.meshgrid(X, Y)\n",
    "W = torch.tensor([[1.0, 0.0]], dtype=torch.float32)\n",
    "b = torch.tensor([0.0], dtype=torch.float32)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "Z = Perceptron(X=X, W=W, b=b, activation=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(1))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('Step function along x0 direction')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:22: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "# 2D Flipped Step function along X-direction\n",
    "W = torch.tensor([[-1.0, 0.0]], dtype=torch.float32)\n",
    "b = torch.tensor([0.0], dtype=torch.float32)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "Z = Perceptron(X=X, W=W, b=b, activation=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(1))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('Flipped Step function along x0 direction')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:29: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "# 2D wave along x-direction\n",
    "X = torch.linspace(start=-1, end=1, steps=100)\n",
    "Y = torch.linspace(start=-1, end=1, steps=100)\n",
    "gridX, gridY = torch.meshgrid(X, Y)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "W0 = torch.tensor([[1.0, 0.0],\n",
    "                    [-1.0, 0.0]\n",
    "                    ], dtype=torch.float32)\n",
    "b0 = torch.tensor([0.5, 0.5], dtype=torch.float32)\n",
    "W1 = torch.tensor([[1.0, 1.0]], dtype=torch.float32)\n",
    "b1 = torch.tensor([-1.5])\n",
    "Z = MLP(X=X, W0=W0, W1=W1, b0=b0, b1=b1, activation0=torch.heaviside, activation1=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(2))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('2D wave along x0 direction')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:29: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "# 2D wave along y-direction\n",
    "X = torch.linspace(start=-1, end=1, steps=100)\n",
    "Y = torch.linspace(start=-1, end=1, steps=100)\n",
    "gridX, gridY = torch.meshgrid(X, Y)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "W0 = torch.tensor([[0.0, 1.0],\n",
    "                    [0.0, -1.0]\n",
    "                    ], dtype=torch.float32)\n",
    "b0 = torch.tensor([0.5, 0.5], dtype=torch.float32)\n",
    "W1 = torch.tensor([[1.0, 1.0]], dtype=torch.float32)\n",
    "b1 = torch.tensor([-1.5])\n",
    "Z = MLP(X=X, W0=W0, W1=W1, b0=b0, b1=b1, activation0=torch.heaviside, activation1=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(2))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('2D wave along x1 direction')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:30: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "X = torch.linspace(start=-1, end=1, steps=100)\n",
    "Y = torch.linspace(start=-1, end=1, steps=100)\n",
    "gridX, gridY = torch.meshgrid(X, Y)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "W0 = torch.tensor([[1.0, 0.0],\n",
    "                    [-1.0, 0.0],\n",
    "                    [0.0, 1.0],\n",
    "                    [0.0, -1.0]\n",
    "                    ], dtype=torch.float32)\n",
    "b0 = torch.tensor([0.5, 0.5, 0.5, 0.5], dtype=torch.float32)\n",
    "W1 = torch.tensor([[1.0, 1.0, 1.0, 1.0]], dtype=torch.float32)\n",
    "b1 = torch.tensor([-2.0])\n",
    "Z = MLP(X=X, W0=W0, W1=W1, b0=b0, b1=b1, activation0=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(2))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('Tower with surrounding plateaus')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ananya.h.a/.virtualenvs/dl_book/lib/python3.7/site-packages/ipykernel_launcher.py:31: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n"
     ]
    }
   ],
   "source": [
    "# 2D Tower\n",
    "X = torch.linspace(start=-1, end=1, steps=100)\n",
    "Y = torch.linspace(start=-1, end=1, steps=100)\n",
    "gridX, gridY = torch.meshgrid(X, Y)\n",
    "X = torch.tensor([(y, x) for y, x in zip(gridX.reshape(-1), gridY.reshape(-1))])\n",
    "W0 = torch.tensor([[1.0, 0.0],\n",
    "                    [-1.0, 0.0],\n",
    "                    [0.0, 1.0],\n",
    "                    [0.0, -1.0]\n",
    "                    ], dtype=torch.float32)\n",
    "b0 = torch.tensor([0.5, 0.5, 0.5, 0.5], dtype=torch.float32)\n",
    "W1 = torch.tensor([[1.0, 1.0, 1.0, 1.0]], dtype=torch.float32)\n",
    "b1 = torch.tensor([-3.5])\n",
    "Z = MLP(X=X, W0=W0, W1=W1, b0=b0, b1=b1, activation0=torch.heaviside, activation1=torch.heaviside)\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.gca(projection=\"3d\")\n",
    "surf = ax.plot_surface(\n",
    "    gridX, gridY, Z.reshape(100, -1).numpy(), cmap=cm.coolwarm,\n",
    "    linewidth=0, antialiased=False\n",
    ")\n",
    "ax.xaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.yaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter(\"%.1f\"))\n",
    "ax.zaxis.set_major_locator(LinearLocator(2))\n",
    "ax.set_zlabel(\"$y(x0, x1)$\", fontsize=20, rotation=0)\n",
    "ax.set_xlabel(\"x0\", fontsize=20)\n",
    "ax.set_ylabel(\"x1\", fontsize=20)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.title('Tower2D')\n",
    "plt.show()\n",
    "fig.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
